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utils_gp_dnn.py
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import numpy as np
import tensorflow as tf
import tensorflow_probability as tfp
import json
# Subclassed GP-DNN marginal likelihood loss function
class GP_DNN_marginal_neglikelihood_loss(tf.keras.losses.Loss):
def __init__(self, noise_var=[0.5, 0.1], corr_coef=np.array([[1, 0.3], [0.3, 1]])):
super().__init__()
self.num_coef = len(noise_var)
self.noise_var = noise_var
self.corr_coef = corr_coef
def call(self, y_true, x_tilde_pred):
y_true_cokrig = tf.concat(
[
tf.expand_dims(
tf.gather(
y_true[:, 0], tf.squeeze(tf.where(y_true[:, -1] == i)), axis=0
),
axis=-1,
)
for i in range(self.num_coef)
],
axis=0,
)
x_tilde_pred_cokrig = [
tf.gather(x_tilde_pred, tf.squeeze(tf.where(y_true[:, -1] == i)), axis=0)
for i in range(self.num_coef)
]
x_tilde_pred_cov = cokriging_covariance(
x_tilde_pred_cokrig,
x_tilde_pred_cokrig,
self.noise_var,
self.corr_coef,
is_training_cov=True,
)
x_tilde_pred_cov = tf.concat(
[
tf.concat(x_tilde_pred_cov[i], axis=-1)
for i in range(len(x_tilde_pred_cov))
],
axis=0,
)
data_fit = 0.5 * tf.linalg.matmul(
tf.linalg.matmul(
y_true_cokrig, tf.linalg.inv(x_tilde_pred_cov), transpose_a=True
),
y_true_cokrig,
)
_, complex_logdet = tf.linalg.slogdet(x_tilde_pred_cov)
complexity = 0.5 * complex_logdet
return tf.squeeze(data_fit + complexity)
# Subclassed GP-DNN likelihood metric
class GP_DNN_likelihood(tf.keras.metrics.Metric):
def __init__(
self,
model,
x_train,
y_train_obs,
noise_var=[0.5, 0.1],
corr_coef=np.array([[1, 0.3], [0.3, 1]]),
eval_var=[0],
name="GP_DNN_likelihood",
**kwargs
):
super(GP_DNN_likelihood, self).__init__(name=name, **kwargs)
self.model = model
self.x_train = x_train
self.y_train_obs = y_train_obs
self.num_coef = len(noise_var)
self.noise_var = noise_var
self.corr_coef = corr_coef
self.eval_var = eval_var
self.krig_likelihood = tf.Variable(-999)
def update_state(self, y_true, x_tilde_pred, sample_weight=None):
###### For user-provided x_train
x_tilde_train = self.model(self.x_train)
x_tilde_train_cokrig = [
tf.gather(
x_tilde_train,
tf.squeeze(tf.where(self.y_train_obs[:, -1] == i)),
axis=0,
)
for i in range(self.num_coef)
]
y_train = tf.concat(
[
tf.expand_dims(
tf.gather(
self.y_train_obs[:, 0],
tf.squeeze(tf.where(self.y_train_obs[:, -1] == i)),
axis=0,
),
axis=-1,
)
for i in range(self.num_coef)
],
axis=0,
)
x_tilde_train_cov = cokriging_covariance(
x_tilde_train_cokrig,
x_tilde_train_cokrig,
self.noise_var,
self.corr_coef,
is_training_cov=True,
)
x_tilde_train_cov = tf.concat(
[
tf.concat(x_tilde_train_cov[i], axis=-1)
for i in range(len(x_tilde_train_cov))
],
axis=0,
)
########
###### For tf-provided x_tilde
y_true_cokrig = tf.concat(
[
tf.expand_dims(
tf.gather(
y_true[:, 0], tf.squeeze(tf.where(y_true[:, -1] == i)), axis=0
),
axis=-1,
)
for i in range(self.num_coef)
],
axis=0,
)
x_tilde_pred_cokrig = [
tf.gather(x_tilde_pred, tf.squeeze(tf.where(y_true[:, -1] == i)), axis=0)
for i in range(self.num_coef)
]
x_tilde_pred_cov = cokriging_covariance(
x_tilde_pred_cokrig,
x_tilde_train_cokrig,
self.noise_var,
self.corr_coef,
is_training_cov=False,
)
x_tilde_pred_pred_cov = cokriging_covariance(
x_tilde_pred_cokrig,
x_tilde_pred_cokrig,
self.noise_var,
self.corr_coef,
is_training_cov=False,
)
####
x_tilde_pred_cov = tf.concat(
[tf.concat(x_tilde_pred_cov[i], axis=-1) for i in range(self.num_coef)],
axis=0,
)
x_tilde_pred_pred_cov = tf.concat(
[
tf.concat(x_tilde_pred_pred_cov[i], axis=-1)
for i in range(self.num_coef)
],
axis=0,
)
x_tilde_train_cov_inv = tf.linalg.inv(x_tilde_train_cov)
y_pred = tf.linalg.matmul(
tf.linalg.matmul(x_tilde_pred_cov, x_tilde_train_cov_inv), y_train
)
y_cov = x_tilde_pred_pred_cov - tf.linalg.matmul(
tf.linalg.matmul(x_tilde_pred_cov, x_tilde_train_cov_inv),
x_tilde_pred_cov,
transpose_b=True,
)
# For numerical stability
epsln = 1e-6
y_cov = y_cov + tf.eye(tf.shape(y_cov)[0], dtype=tf.float64) * epsln
try:
self.krig_likelihood = -tfp.distributions.MultivariateNormalTriL(
loc=tf.squeeze(y_pred), scale_tril=tf.linalg.cholesky(y_cov)
).log_prob(tf.squeeze(y_true_cokrig))
except:
self.krig_likelihood = np.nan
######
def result(self):
return self.krig_likelihood
# Subclassed GP-DNN RMSE metric
class GP_DNN_RMSE(tf.keras.metrics.Metric):
def __init__(
self,
model,
x_train,
y_train_obs,
noise_var=[0.5, 0.1],
corr_coef=np.array([[1, 0.3], [0.3, 1]]),
eval_var=[0],
name="GP_DNN_RMSE",
**kwargs
):
super(GP_DNN_RMSE, self).__init__(name=name, **kwargs)
self.model = model
self.x_train = x_train
self.y_train_obs = y_train_obs
self.num_coef = len(noise_var)
self.noise_var = noise_var
self.corr_coef = corr_coef
self.eval_var = eval_var
self.krig_RMSE = tf.Variable(-999)
def update_state(self, y_true, x_tilde_pred, sample_weight=None):
###### For user-provided x_train
x_tilde_train = self.model(self.x_train)
x_tilde_train_cokrig = [
tf.gather(
x_tilde_train,
tf.squeeze(tf.where(self.y_train_obs[:, -1] == i)),
axis=0,
)
for i in range(self.num_coef)
]
y_train = tf.concat(
[
tf.expand_dims(
tf.gather(
self.y_train_obs[:, 0],
tf.squeeze(tf.where(self.y_train_obs[:, -1] == i)),
axis=0,
),
axis=-1,
)
for i in range(self.num_coef)
],
axis=0,
)
x_tilde_train_cov = cokriging_covariance(
x_tilde_train_cokrig,
x_tilde_train_cokrig,
self.noise_var,
self.corr_coef,
is_training_cov=True,
)
x_tilde_train_cov = tf.concat(
[
tf.concat(x_tilde_train_cov[i], axis=-1)
for i in range(len(x_tilde_train_cov))
],
axis=0,
)
########
###### For tf-provided x_tilde
y_true_cokrig = [
tf.expand_dims(
tf.gather(
y_true[:, 0], tf.squeeze(tf.where(y_true[:, -1] == i)), axis=0
),
axis=-1,
)
for i in range(self.num_coef)
]
x_tilde_pred_cokrig = [
tf.gather(x_tilde_pred, tf.squeeze(tf.where(y_true[:, -1] == i)), axis=0)
for i in range(self.num_coef)
]
x_tilde_pred_cov = cokriging_covariance(
x_tilde_pred_cokrig,
x_tilde_train_cokrig,
self.noise_var,
self.corr_coef,
is_training_cov=False,
)
######
rmses = []
for i in self.eval_var:
x_tilde_pred_cov1 = tf.concat(x_tilde_pred_cov[i], axis=-1)
krig_weights = tf.linalg.solve(
x_tilde_train_cov, tf.transpose(x_tilde_pred_cov1)
)
y_pred = tf.linalg.matmul(tf.transpose(krig_weights), y_train)
rmses.append(tf.sqrt(tf.reduce_mean((y_pred - y_true_cokrig[i]) ** 2)))
self.krig_RMSE = tf.reduce_mean(rmses)
######
def result(self):
return self.krig_RMSE
# Function for constructing covariance matrix
def cokriging_covariance(
x_tilde_pred, x_tilde_train, noise_var, corr_coef, is_training_cov
):
num_coef = len(noise_var)
x_tilde_cov = [[None for j in range(num_coef)] for i in range(num_coef)]
for i in range(num_coef):
for j in range(i + 1):
if i == j:
x_tilde_cov[i][j] = tfp.math.psd_kernels.MaternFiveHalves().matrix(
x_tilde_pred[i], x_tilde_train[j]
)
if is_training_cov:
x_tilde_cov_diag = tf.linalg.diag_part(x_tilde_cov[i][j])
x_tilde_cov[i][j] = tf.linalg.set_diag(
x_tilde_cov[i][j],
x_tilde_cov_diag
+ noise_var[i] * tf.ones_like(x_tilde_cov_diag),
)
else:
x_tilde_cov[i][j] = tf.sign(
corr_coef[i, j]
) * tfp.math.psd_kernels.MaternFiveHalves(
amplitude=tf.sqrt(tf.abs(corr_coef[i, j]))
).matrix(
x_tilde_pred[i], x_tilde_train[j]
)
for i in range(num_coef - 1):
for j in range(i + 1, num_coef):
if is_training_cov:
x_tilde_cov[i][j] = tf.transpose(x_tilde_cov[j][i])
else:
x_tilde_cov[i][j] = tf.sign(
corr_coef[i, j]
) * tfp.math.psd_kernels.MaternFiveHalves(
amplitude=tf.sqrt(tf.abs(corr_coef[i, j]))
).matrix(
x_tilde_pred[i], x_tilde_train[j]
)
return x_tilde_cov
class NpEncoder(json.JSONEncoder):
def default(self, obj):
if isinstance(obj, np.integer):
return int(obj)
if isinstance(obj, np.floating):
return float(obj)
if isinstance(obj, np.ndarray):
return obj.tolist()
return super(NpEncoder, self).default(obj)